Slide 1

lovinggudgeonMécanique

22 févr. 2014 (il y a 3 années et 1 mois)

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Titan’s Ontario Lacus: Smoothness
Constraints from Cassini RADAR

Lauren Wye, Howard Zebker

Stanford University

with contributions from members of the Cassini

RADAR Team

Outline


Titan, Lakes and Ontario Lacus


Radar scattering theory for lake surfaces


T49 Altimetry Observation (Dec 21, 2008)


T49 backscatter and roughness results


Implications for lake material and winds


12/02/2009

2

L. Wye

3

Image Credit: NASA

98% Nitrogen

100% cloud cover

200
-
880 km

Atmosphere

77% Nitrogen

50% cloud cover

100 km

Atmosphere

1 g

1.0 bars

290 K (60 F)

Surface

Surface

Earth

Titan

5,150 km

12,715 km

0.14 g

1.5 bars

94 K (
-
290F)

4

The Cassini RADAR uses 2.2 cm
-
λ

signals to
penetrate the haze and explore the surface.

Frequency (Wavelength)

13.78 GHz (2.18 cm)

Power Transmitted

48.084 W

Peak Gain

50.7 dB

Beamwidth (one
-
way)

0.373º

High
-
Gain Antenna Area

4.43 m
2


Polarization

same
-
sense linear (SL)


Cassini RADAR Instrument Parameters

The RADAR operates in four primary modes.

Scatterometry

Mode:

Backscatter
response
and
mapping

Radiometry Mode:

Brightness temperatures and emissivity

SAR Mode:

Imaging at resolutions 350


1000 m


Altimetry Mode:

Heights with vertical resolution 35
-
50 m

Janssen et al.,
Icarus

2009.

6

Erosion and Channels

Dunes

Craters

Cryovolcanic flows

Mountain Chains

Credit: NASA/JPL

7

Liquid Hydrocarbons

North Polar Region

Credit: NASA/JPL

12/02/2009

L. Wye

8

Lakes are prevalent in Titan’s north polar region.


Credit: NASA/JPL/USGS

About 10% of
mapped area
appears to be
liquid.

About 55% of
the north has
been mapped.

Kraken
Mare

Ligeia

Mare

90
°
W

0
°
W

90
°
N

80
°
N

70
°
N

About 60% of the south polar region has been
imaged, but only 0.4% appears to be liquid.

Due to
asymetry

in seasons from Saturn’s orbital configuration? (Aharonson, et al.)

Ontario Lacus

12/02/2009

9

Credit: A. Hayes

180
°
W

Asymmetric distribution
of lakes

12/02/2009

10

Aharonson et al., Nature
Geoscience
, 2009.

10%

0.7%

1.0%

0.40%

0.10%

0.36%

NORTH

SOUTH

Asymmetry in Titan’s
seasons may cause
dichotomy: hotter, shorter
southern summers may
drive volatiles to north

Ontario Lacus was discovered by ISS in Jun
2005 and imaged by VIMS in Dec 2007.

22,000 km
2

235 km x 73 km

Barnes et al.,
Icarus

2008

Cassini ISS

11

Annuli interpreted as past shorelines:
time
-
dependence requires presence of
liquid methane (in addition to the liquid
ethane present in the spectra).



0
0.005
0.01
0.015
0.02
RADAR imaged Ontario Lacus in June (T57) and
July (T58) 2009, revealing a complex shoreline
and non
-
uniform surface.



0
0.005
0.01
0.015
0.02
25
30
35
40
45
0
0.005
0.01
0.015
0.02
Incidence Angle
Sigma-0
SAR Beam
Footprint

The nearly
-
flat slope of the dark section implies that there is very
little diffuse scattering in the liquid itself, but these values are
near the noise
-
equivalent sigma
-
0 level and are suspect.

T57

T58

12/02/2009

12

L. Wye

RADAR Ontario
Observations

12/02/2009

L. Wye

13

Wall et al., submitted to GRL.

A: Flooded valleys

C: Wave
-
generated raised beach

D: River Valley

E: Alluvial Fan

F: Recently flooded
diapiric

structure

I: 1km wide river channel

J,K: Delta lobes

L: Flooded valley system

Shoreline receded by 10 km over 4 years
since ISS image; 1 m/year flux in depth
consistent with GCM methane evaporation
rates (Hayes et al., submitted to
Icarus
).

18,700 km
2

T49 data

88.5K T
b
→90
-
92 K T
s

<10m over 100 m

Radar imaging is typically acquired at angles > 20
°
. For
smooth surfaces (e.g. lakes), this means that the signal
is reflected away from the radar and is never received.

72
°

S, 184
°

W

173 km


198 km

Ontario
Lacus

Liquid Smooth Surface

No signal
received


i

Specular

reflection away
from radar

Strong signal
received
(diffuse)

Solid or Liquid Rough
Surface


i

Small
specular

reflection away
from radar

12/02/2009

14

By observing near
-
nadir (T49), where surface
scattering dominates, we can constrain the
roughness of the surface.

Liquid Smooth Surface


i

→ 0
°

Specular

reflection
towards radar

Liquid Smooth Surface

No signal
received


i

Specular

reflection away
from radar

Strong signal
received
(diffuse)

Solid or Liquid Rough
Surface


i

Small
specular

reflection away
from radar

Small
specular

reflection
towards radar
and

diffuse reflection

Solid or Liquid Rough
Surface


i

→ 0
°

Very strong
signal received

Extremely
strong signal
received

12/02/2009

15

L. Wye

0.37
°

12 km

0.37
°

R=1850 km

12 km

109 m

Rough Surface

Smooth Surface

Fresnel radiation pattern

The near
-
nadir echo from a surface that is
rough at wavelength and larger scales
comprises quasi
-
specular

scatter radiated by
all illuminated facets facing the radar.

The near
-
nadir echo from a surface that is
very

smooth

comes

primarily from the
first Fresnel zone (~1% of the beam
diameter); All other zones will cancel out.



The total echo is the sum of the scattered signals
over the entire beam; this tends toward a
Gaussian distribution via central limit theorem.

Gaussian Histogram

Like that of a single point
scatterer
, the received
echo is a replica of the transmitted waveform, with
reduced amplitude and modified phase.

Sinusoid Histogram

2
1
R
F




a
R
a
R
F


2
1

a = 2575 km

First Fresnel zone radius

Planar surface

Curved surface

12/02/2009

16

L. Wye

A lake burst’s histogram is very different from the surrounding
surface’s histogram: it has a sinusoidal shape, which corresponds
to a perfect coherent reflection of the transmitted chirp signal.

-150
-100
-50
0
50
100
150
0
0.2
0.4
0.6
0.8
1
Histogram Bin
-150
-100
-50
0
50
100
150
0
0.2
0.4
0.6
0.8
1
Histogram Bin
Burst 103 (Lake)

Burst 300 (Surface)

The Lake echo is saturated: discrete quantization effect and asymmetry from DC bias.

12/02/2009

17

L. Wye

The stacked T49 data histograms illustrate the unique
sinusoidal characteristic of the lake (Bursts 100
-
200).

Histogram Bin
T49 Altimetry Burst Index


-100
-50
0
50
100
50
100
150
200
250
300
350
400
450
0
200
400
600
800
1000
Histogram Bin
Altimetry Echo Index


-100
-50
0
50
100
100
150
200
250
0
200
400
600
800
1000
12/02/2009

18

L. Wye

The received pulse echo looks like a
chirped sinusoid...

12/02/2009

L. Wye

19

0
200
400
600
800
1000
1200
1400
1600
1800
2000
-150
-100
-50
0
50
100
150
Sample Index
Measured Voltage (dn)
Receive Window for First Pulse Echo
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-150
-100
-50
0
50
100
150
Sample Index
Measured Voltage (dn)
Receive Window for First Pulse Echo
Only it is severely clipped.

12/02/2009

L. Wye

20

The received lake signal is saturated: all 15
pulse echoes are clipped to
±
145.8
dn

12/02/2009

L. Wye

21

0
0.5
1
1.5
2
2.5
3
x 10
4
0
50
100
150
Sample Index
Measured Voltage Amplitude (dn)
Receive Window for T49 burst 2040
The received lake signal is saturated: all 15
pulse echoes are clipped to 145.8
dn

12/02/2009

L. Wye

22

Sample Index within Pulse
Pulse Index
Measured Voltage Amplitude (dn)


500
1000
1500
2000
2
4
6
8
10
12
14
0
20
40
60
80
100
120
140
0
0.5
1
1.5
2
2.5
3
x 10
4
0
50
100
150
Sample Index
Measured Voltage Amplitude (dn)
Receive Window for T49 burst 2040
0
500
1000
1500
2000
0
50
100
150
Measured Voltage Amplitude (dn)
Sample Index
First Pulse Echo

The Block Adaptive Quantization algorithm is based on
Gaussian sample statistics and a periodic echo profile.

8
-
2 BAQ Decode

8
-
2 BAQ Encode

BAQ

X
0

X

8 bits

8 bits

(2 bits,
Th
)

12/02/2009

23

L. Wye

X

The algorithm is similar for 8
-
4 bits but with 16 levels.

If echo profile is periodic, then similar blocks
(red) are sampling the same surface and can
calculate standard deviation (threshold).

Typical altimetry data utilizes all 16 encoded words.

0
0.5
1
1.5
2
2.5
3
x 10
4
0
5
10
15
Received sample
Encoded 4-bit value
12/02/2009

24

L. Wye

By simulating the BAQ algorithm, we show that a
saturated signal will only utilize 10 encoded words.

0
0.5
1
1.5
2
2.5
3
x 10
4
0
5
10
15
Received sample
Encoded 4-bit value
And because the threshold is fixed to its maximum value (255), the 10 levels
will always be the same, no matter the signal.

12/02/2009

25

We model the bursts that show a strong sinusoidal
signature (>50% of their echo falls within the 10
histogram bins characteristic of a quantized sinusoid).

50
100
150
200
250
300
350
400
450
0
10
20
30
40
50
60
70
80
90
100
T49 Altimetry Burst Index
Percent Sinusoidal
12/02/2009

26

L. Wye

0
100
200
300
400
500
0
10
20
30
40
50
60
70
80
T49 Altimetry Burst Index
Measured Sigma-0
Sigma-0 assuming range/area/attenuation dependence


CF
A
dS
G
N
P
R
C
E
r
ptx
t
adn
r











2
2
)
(
0
4
The jump is due to an attenuation
change and the slope is from range and
area variations.

(Issue 3) The saturated signal does not show a
dependence on range, area, or attenuation.

12/02/2009

27

L. Wye

We consider the most saturated sinusoidal bursts (
red
) as
candidates for the ‘true’ sigma
-
0 levels.

0
100
200
300
400
0
10
20
30
40
50
60
70
80
T49 Altimetry Burst Index
Sigma-0
0
100
200
300
400
0
10
20
30
40
50
60
70
80
T49 Altimetry Burst Index
Sigma-0
The lowest s0 level is
obtained using from
burst 125 (gray circle),
right before the
attenuator jump.

The highest s0 level is obtained using the parameters from
burst 126 (black circle), right after the attenuator jump.

12/02/2009

29

L. Wye

BAQ

To correct for saturation error, we must understand
the effect of the receiver on the output signal.

Modified from West
et al., 2008

Quantizes to 8 bits

Compresses to 4 bits

The saturating signal may
incur some distortion in here.

12/02/2009

30

L. Wye

We use histogram matching to correct for some
of the saturation error.

Simulate transmitted signal: Sinusoid with amplitude
(A)

Subtract dc Offset
(
DCoffset
)

Apply input
-
output receiver transformation
(maybe more
params
)

Clip signal to
+

127.5 (8
-
bit quantized)

Apply 8
-
4 BAQ

Compare output histogram to data histogram

12/02/2009

31

L. Wye

-500
-400
-300
-200
-100
0
100
200
300
400
500
-150
-100
-50
0
50
100
150
Soft Clip Limiter Model
Input Amplitude
Output Amplitude
Hard Clip

Soft Clip (p=10)

Soft Clip (p=5)

Soft Clip (p=2)

p
p
K
x
x
y
1
1
















0
20
40
-200
-150
-100
-50
0
50
100
150
200
time
signal
Effect on Sinusoid

Hard Clip vs. Soft Clip Limiter Model

12/02/2009

32

L. Wye

The saturated lake histograms cannot be
reproduced with a simple hard clipper; signal
distortion is required.

-150 -100 -50 0 50 100 150
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Histogram Bin
Hard Clip Model fit to T49 b2000
-150
-100
-50
0
50
100
150
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Histogram Bin
Soft Clip Model (P1P2K1K2post) fit to T49 b2000
A = 395.8

DC offset = 57.6

P1 = 2.72

P2 = 0.82

K1 = 248.7

K2 = 354.4

SSE = 1.1e
-
4

A = 298.6

DC offset = 47.7

SSE = 2.9e
-
3

12/02/2009

33

L. Wye

50
100
150
200
0
200
400
600
800
1000
T49 altimetry echo burst index
Peak voltage amplitude (dn)
Using these models, we estimate the original input
signal levels of the saturated lake echoes (for echoes
with >50% sinusoidal histogram indicator).

80
100
120
140
160
180
200
200
400
600
800
1000
T49 Altimetry Burst Index
Peak Amplitude
60
80
100
120
140
160
180
200
200
400
600
800
1000
T49 Altimetry Burst Index
Peak Amplitude
12/02/2009

34

L. Wye

To make sense of this, we have engineering
data from T56. As we decrease the
attenuation, the signal begins to saturate.

Histogram Bin
Burst Index
T56 8-8 Histograms (Normalized)


-100
-50
0
50
100
1
2
3
4
5
6
7
8
9
10
0
0.002
0.004
0.006
0.008
0.01
Histogram Bin
Burst Index
T56 8-8 Histograms (Normalized)


-100
-50
0
50
100
1
2
3
4
5
6
7
8
9
10
0
0.2
0.4
0.6
0.8
1
Histogram Bin
Burst Index
T56 8-4 BAQ Histograms (Normalized, Logarithmic)


-100
-50
0
50
100
15
20
25
30
-25
-20
-15
-10
-5
0
Histogram Bin
Burst Index
T56 8-8 Histograms (Normalized, Logarithmic)


-100
-50
0
50
100
1
2
3
4
5
6
7
8
9
10
-35
-30
-25
-20
-15
-10
-5
0
-
61 dB

-
43 dB

-
61 dB

-
43 dB

12/02/2009

35

L. Wye

100
200
300
400
500
600
200
400
600
800
1000
1200
1400
Modeled Output Amplitude
Theoretical Input Amplitude
T56 8-4 BAQ Soft Clip (P1P2K1K2pre) Model Response
Using the T56 best
-
fit model results, we develop a method
of correcting and bounding the overestimated amplitudes.

100
150
200
250
300
350
400
450
500
550
600
100
150
200
250
300
350
400
450
500
550
600
Modeled Output Amplitude
Theoretical Input Amplitude
T56 8-4 BAQ Hard Clip Model Response
We linearly map the
estimated amplitudes from
149 to 850 to their
corresponding input
amplitudes

For estimated amplitudes > 850,
where the estimator “plateaus”, we
bound to the highest unambiguous
input amplitude (245)

12/02/2009

36

L. Wye

60
80
100
120
140
160
180
200
200
400
600
800
1000
T49 Altimetry Burst Index
Peak Amplitude
Using the amplitude correction algorithm from T56,
we estimate the lower bounds of the T49 lake
amplitudes (yellow).

80
100
120
140
160
180
200
200
400
600
800
1000
T49 Altimetry Burst Index
Peak Amplitude
1.57x increase in lower bound s0

12/02/2009

37

L. Wye

50
100
150
200
0
200
400
600
800
1000
T49 altimetry echo burst index
Peak voltage amplitude (dn)
Measured Amplitudes

Hard Clip Model

Soft Clip Model

Bound Corrected Amplitudes

West Longitude
Latitude


195
190
185
180
175
170
-67.5
-70
-72.5
-75
-77.5
0
10
20
30
40
50
60
70
80
100
200
300
400
0
20
40
60
80
Along Track Distance (km)
Sigma-0
Normalized radar
cross section (

0

)



0



10
20
30
40
50
60
70
80
Normalized by beam
-
illuminated area

Sigma
-
0 Results (Lower Bound)

12/02/2009

38

L. Wye

From geometric optics, we expect the radar cross section to be:



2
2
2
R
a
R
a




2
1
1














R = ~1900 km

a = 2575 km

)
GO
(
)
measured
(
0
0



S




2
4
2
2
2





h
e
R
a
R
a



If the surface is not perfectly smooth,

the cross section will be
exponentially reduced.

12/02/2009

39

L. Wye

0.37
°

12 km

109 m

A smooth surface can be slightly roughened (up to ~1/4


rms

height) and still maintain its coherent
specular

nature.

As the surface roughens, the transmitted sinusoid will
reflect from points of different heights (phase delays) within
the Fresnel zone. These reflected sinusoids will interfere,
reducing the perceived amplitude of the received signal.

Fresnel radiation pattern

0
2
4
6
8
10
0
0.2
0.4
0.6
0.8
1
RMS surface height (mm)
Normalized measured amplitude
The measured amplitude falls off
exponentially with increasing roughness.





t
j
k
j
t
j
e
e
S
d
e
e
S
h
h






















2
e
2
2
2
8
h
2
-
2
12/02/2009

40

L. Wye

100
150
200
250
300
2.4
2.6
2.8
3
3.2
3.4
Along Track Distance (km)
RMS Surface Height (mm)
West Longitude
Latitude


195
190
185
180
175
170
-67.5
-70
-72.5
-75
-77.5
2.8
2.85
2.9
2.95
3
3.05
3.1
RMS Surface Heights

(



ㄮ1)



= 2.4



= 1.9



㴠=⸶



2.8
2.85
2.9
2.95
3
3.05
3.1
RMS Heights for
Specular
-
only points

12/02/2009

41

L. Wye

100
150
200
250
300
2.4
2.6
2.8
3
3.2
3.4
Along Track Distance (km)
RMS Surface Height (mm)
West Longitude
Latitude


195
190
185
180
175
170
-67.5
-70
-72.5
-75
-77.5
2.8
2.85
2.9
2.95
3
3.05
3.1
RMS Surface Heights

(



ㄮ1)



= 2.4



= 1.9



㴠=⸶



2.8
2.85
2.9
2.95
3
3.05
3.1
RMS Heights (for
Specular
-
only points)
must be
less than

3 mm over ~100 m

Suggests waves are not present





2
4
2
2
2





h
e
R
a
R
a



12/02/2009

42

L. Wye

Photometric models fit to VIMS brightness (5

μ
m)
suggest Ontario is quiescent and smooth, free of
scattering centers larger than a few
μ
m.

12/02/2009

L. Wye

43

Brown et al., Nature 2008

Lake Interior

Adjacent area outside of Lake

Lake has ~zero reflectivity
at zero
airmass


Waves should be easy to generate on Titan:


Higher air density of Titan (4x denser than Earth) lowers
the threshold wind speed to 0.5
-
1 m/s (Lorenz et al.,
submitted
Icarus
)


Low density and low viscosity liquid hydrocarbons should
facilitate wave generation


Lower gravity (14% of Earth’s) should allow 7x larger
wave heights for fully developed seas of a given wind
speed (
Ghafoor

et al., JGR 2000)


For 1 m/s winds, models suggest
rms

wave heights > 2.5
cm (
Ghafoor
; Notarnicola et al. 2009); 0.3 m/s needed to
generate our upper limit



12/02/2009

L. Wye

44

Liquid hydrocarbons (with low viscosity and low
density) and the higher Titan air pressure should
facilitate significant capillary wave generation.

12/02/2009

45

Lorenz et al.,
Icarus

175, 2005.

“Sea
-
surface wave growth under extraterrestrial atmospheres:

Preliminary wind tunnel experiments with applications to Mars and Titan.”

Waves should be easy to generate on Titan:


Higher air density of Titan (4x denser than Earth) lowers
the threshold wind speed to 0.5
-
1 m/s (Lorenz et al.,
submitted
Icarus
)


Low density and low viscosity liquid hydrocarbons should
facilitate wave generation


Lower gravity (14% of Earth’s) should allow 7x larger
wave heights for fully developed seas of a given wind
speed (
Ghafoor

et al., JGR 2000)


For 1 m/s winds, models suggest
rms

wave heights > 2.5
cm (
Ghafoor
; Notarnicola et al. 2009); 0.3 m/s needed to
generate our upper limit



12/02/2009

L. Wye

46

This combined with morphological evidence of wave action at
some time in the past on one shore of Ontario Lacus

Implications for winds and material properties
(from Lorenz et al., submitted to
Icarus
)


Threshold wind speed for capillary wave
generation on
Earth
: 1
-
2 m/s


On
Titan
(scaling by air density only): ~0.5
-
1
m/s for pure methane/ethane/nitrogen


These winds (over >20 km fetch) should lead to
gravity waves of 20 cm height.


Threshold can be increased by factor of 2 or
more from change in liquid properties

12/02/2009

47

L. Wye

Winds are low (<0.5 m/s) during radar
observations of Ontario Lacus

Lorenz, Newman, Lunine, Threshold of Wave Generation on Titan’s Lakes and Seas:
Effect of Viscosity and Implications for Cassini Observations, submitted to
Icarus
.

TitanWRF

by
Claire Newman

12/02/2009

48

L. Wye

Winds should pick up in upcoming
northern observations.

12/02/2009

49

Lorenz, Newman, Lunine, Threshold of Wave Generation on Titan’s Lakes and Seas:
Effect of Viscosity and Implications for Cassini Observations, submitted to
Icarus
.

VIMS
specular

detection (July, 2009):
Stephan et al. AGU
Fall09.

Viscosity likely higher than predicted for clean
liquid hydrocarbons: affect wave generation
threshold by factor >2 (Lorenz et al, submitted)


Deposits of dissolved heavy hydrocarbons
expected (
Cordier

et al., submitted) which have
viscosities 5x larger than pure liquid
hydrocarbons.


Suspended sediment (such as fine
-
grained
tholin

haze with low sedimentation velocity) may
increase bulk viscosity


Possible that Ontario may be more viscous than
northern lakes (transport of methane/ethane)

12/02/2009

L. Wye

50

0
0.1
0.2
0.3
0.4
0.5
0
10
20
30
40
50
60
70
80
Volume Fraction of Suspended Particles
Scaled Dynamic Viscosity
Lab data: As the volume fraction of suspended
particles approaches 45
-
50%, the viscosity
diverges (increases to >50x original velocity).

12/02/2009

L. Wye

51

Halder

et al., J. Phys.:
Condens
. Matter 9, 8873
-
8878, 1997.

“The change of viscosity with concentration of suspended particles and a new concept of
gelation
.”

Liquid:
Polydimethyl

siloxane

(PDMS)

-

21.21, 32.47 poise


Suspended Particles:

-

powdered silicon (1
μ
m)

-

powdered glass (14
μ
m)

Hydrodyamic

interaction between the
particles (independent of size and shape)
will begin to arrest the flow as the
number of particles increases.


Fluid Immobilized at a volume fraction
near 0.53.


Results seem independent of liquid.

Summary of Results


We’ve detected a reflected signal from the lake that
mirrors the transmitted signal. A very smooth surface
is needed to produce such a
specular

reflection.


We’ve estimated a lower bound on radar cross section.


We’ve developed a scattering model that relates the
attenuated echo to the
rms

surface roughness (upper
bound) for candidate materials.


The surface is smooth to the order of 3 mm, possibly
further evidence for a liquid material.


These results are consistent with the low wind speeds
predicted by global circulation models and do not
necessarily require increased viscous damping

12/02/2009

52

L. Wye